With electrolysis devices of the type being discussed here, and which operate with an electrolyzer with a polymer electrolyte membrane (PEM) and serve for the production of hydrogen, it is counted as belonging to the state of the art to lead the water, in particular distilled water which is necessary for the operation of the electrolyzer, in a circuit (circulation). Thereby, the water which exits from the PEM electrolyzer typically designed as a stack and which exits at the oxygen side, is firstly led back into a storage means and from there back to the stack. In order to protect the sensitive polymer electrolyte membrane from contamination, the water is freed from metal ions by way of an ion exchanger before entry into the electrolyzer, wherein these ions, even if only in small quantities, are present in the water exiting from the stack. The water fed to the ion exchanger on the one hand is cooled by way of a heat exchanger, and on the other hand warm, distilled water is drained and cold distilled water is fed into the circuit at regular intervals, due to the fact that the ion exchanger is heat-sensitive and can only be operated up to a temperature of approx. 60° C. In practice, this leads to about double the amount of distilled than would actually be required for operation of the PEM electrolyzer being led to into the circuit.